Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
You are told that $\int_{0}^{a} \left( \frac{1}{2} e^{3x} + x^2 \right) \, dx = 10$, with $a$ a positive constant.
(i)[4]
Show, by rearranging, that $a = \frac{1}{3} \ln (61 - 2a^3)$.
(ii)[2]
Show, by calculation, that $a$ lies between $1.0$ and $1.5$.
(iii)[3]
Apply an iterative formula based on the equation in part (i) to determine $a$ correct to $3$ decimal places. Present each iteration to $5$ decimal places.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Carry out the integration to obtain $ke^{3x}+mx^3$” …